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Linear dependence of powers of linear forms
- Source :
- Annales Mathematicae Silesianae, Vol 29, Iss 1, Pp 131-138 (2015)
- Publication Year :
- 2015
-
Abstract
- For a finite set of polynomials F={fj}, B. Reznick [in Algorithmic and quantitative real algebraic geometry (Piscataway, NJ, 2001), 101–121, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 60, Amer. Math. Soc., Providence, RI, 2003; MR1995017] introduced the ticket T(F)={d∈N:{fdj} is linearly dependent}. Motivated by results in the above paper, the author of the current paper studies the "degree'' of linear dependence of the set of powers of polynomials within its ticket, i.e., dimspan{fdj} for d∈T(F). This seems to be a rather difficult question for an arbitrary set of polynomials. The author therefore focuses on the special case when the polynomials are linear forms and proves various interesting results. The interested reader should consult the paper for the details.
- Subjects :
- Pure mathematics
Sums of powers
lcsh:Mathematics
General Mathematics
Linear form
General Medicine
11E76
lcsh:QA1-939
System of linear equations
15A99
Upper and lower bounds
Combinatorics
Sums of powers of linear forms
Dimension (vector space)
Linear independence
Ticket of the set of polynomials
Linear combination
Mathematics
Vector space
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Annales Mathematicae Silesianae, Vol 29, Iss 1, Pp 131-138 (2015)
- Accession number :
- edsair.doi.dedup.....2b9de75337cfd43f4f6528f6a98e2d7d